No idea about client but in browser common issues can be adblock, pop-up block stuff, cookies and cache reset, active VPN, browser turbo mode or sometimes clearing adobe flash cache helps. Reinstall flash at times does not delete all folders and files completely so you should try this:

Be aware that I am not an official support, but from experience can give this advice to try. Have zero problems btw, so its prob not from oasis side, cause all works well for me and for most people. In very very rare cases internet provider can be the cause of this because one time I got DC a lot in one specific game while having no problems in others and it was from the providers side and they fixed it in time, but prob this is not the case here.
P.S - one time, only once during the entire week I had a fail to load in browser at 100% but I refreshed and all was okay. I play from both client and browser so no problems. Edge browser nowadays and have Chrome, also no problems.

What update? Flash player updated? I guess yes from other posts. Prob flash devs broke smth with their update, you should ask their support I suppose if they have it or download an older version of flash. No idea why it asks players to update, never asked anything for me and I don't recall seeing any updates pop-up. My version is 32.0.0.330 and it shows the newest is 32.0.0.387. Hopefully don't need to update anything.

Some advice also include:

1. Fix 1: Make sure to enable Flash Player in Chrome.
2. Fix 2: Make sure to allow Flash Player on the website.
3. Fix 3: Update your Chrome browser and Flash Player. Update Chrome. Update Flash Player.
4. Fix 4: Update graphics card driver.
5. Fix 5: Reinstall Flash Player.
6. Fix 6: Clear browser cache.
   
   All drivers up to date? Maybe an older version of graphic card driver has conflict with a newer flash.

As an experiment I updated to the last version of Adobe Flash. Restarted browser, cleared cache and still everything works at a 1000% clear. No idea what can cause this even if you did everything correctly and every part of your driver is up-to-date. Very weird.
If all drivers are updated for graphics card you can try to delete adobe, clear its cache and type in into google "Archived Adobe Flash player versions". Try downloading an older version of flash from their official site as they store them and allow to download.

Make sure your windows is up to date with its updates also if you use WIN 10. In addition, its a very simple thing, but make sure javascript is allowed in your browser also the same way you allow Flash Player. If not - enable.